England's Football Association is investigating claims around 15 people were involved in a physical altercation after Mourinho complained about the volume of Manchester City's dressing-room celebrations.
Mourinho had a carton of milk thrown at him before a melee ensued involving players and staff in which City coach Mikel Arteta was left with a cut below his eye after being hit by a plastic bottle.
Asked about reports the bottle that hit Arteta was thrown by United striker Romelu Lukaku, Mourinho said: "Accuse? Prove? Show evidence and punish him."
City manager Pep Guardiola, whose side won the game 2-1, has also defended his players, although he has offered an apology to United.
Some City staff have claimed one of their physiotherapists was punched during the ruck, which took place in a corridor leading away from the tunnel, but United have denied their players threw punches.
Mourinho said he was certain his players had not done anything untoward.
"I know," said the United manager. "I am not confident: I know."
When a reporter asked Mourinho if he feared punishment over the brawl, he responded: "I think you work for another club and not for the press."
The FA has given both clubs until 6pm local time (1800 GMT) on Wednesday to offer their accounts of what happened and will then decide whether to act.
Mourinho has a history of passionate celebrations himself.
He ran down the touchline at Old Trafford to celebrate after his Porto side knocked United out of the Champions League in 2004.
He also raced onto the Camp Nou pitch with his arm raised in the air when his Inter Milan team defeated Barcelona -- then coached by Guardiola -- in a 2010 Champions League semi-final.
But Mourinho says his current side are much more restrained, pointing to the way they celebrated their recent 3-1 win at Arsenal.
- 'No respect' -
"What we did in the Arsenal stadium, you know? It was completely diverse (different)," he said.
"What we did, what happened after that match, the way we behaved as winners."
Guardiola had earlier admitted he "encouraged" his players to celebrate, but denied their behaviour was provocative.
"We won a derby. If we offended United -- not just one player, not just Jose, (but) Manchester United -- then I apologise," he said.
"Sometimes United made a lot of celebrations in the past over City. All the managers celebrate sometimes. We have to enjoy those moments.
"What happened in the locker room happened. Hopefully it is never going to happen again.
"If we were not correct, then I apologise to all of Manchester United. Our intentions was not that. It was to celebrate inside the locker room. If the people cannot understand that, then I'm sorry."
He added: "To celebrate with your fans is part of it. In Germany, everyone goes over if you win or lose. I said when I arrived that winning or losing, you have to go over when you are away to say 'thank you'.
"The last action was in the corner (in front of City's fans) and we celebrated there in a normal way -- nothing exceptional."
United host Bournemouth on Wednesday, when they will begin the task of trying to chip away at City's huge 11-point lead in the Premier League.
Speaking to newspaper reporters at United's Carrington training ground on Tuesday, Mourinho became visibly agitated by repeated questioning about the City brawl.
At the end of the briefing, as he left the room, he berated journalists for not asking him more questions about Bournemouth.
"You don't like Bournemouth, hey?" he asked.
"You don't respect them? You don't think they are a team capable of coming to Old Trafford and doing well? No respect for (Bournemouth manager) Eddie Howe? No respect for the players?"